Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
69701	Find the Derivative - d/dx	-5/(x^3)*e^(-3x^4+4x^2)	$- \frac{5}{x^{3}} \cdot e^{- 3 x^{4} + 4 x^{2}}$
69702	Find the Tangent Line at (1,-1)	(x-y-1)^3=x , (1,-1)	${(x - y - 1)}^{3} = x$ , $(1, - 1)$
69703	Find dy/dx	x^2+4y^2=7+3xy	$x^{2} + 4 y^{2} = 7 + 3 x y$
69704	Find the Maximum/Minimum Value	f(x)=-2+24x^2+72x^3-30x^4	$f (x) = - 2 + 24 x^{2} + 72 x^{3} - 30 x^{4}$
69705	Find dy/dθ	y=e^(tan(theta))	$y = e^{\tan (θ)}$
69706	Find the Derivative - d/dz	square root of x^2+y^2+z^2	$\sqrt{x^{2} + y^{2} + z^{2}}$
69707	Integrate Using u-Substitution	integral of sin(x)^2 with respect to x	$\int \sin^{2} (x) d x$
69708	Find dy/dx	x+y=xy	$x + y = x y$
69709	Find the Derivative - d/dx	(x^2)/(2 square root of x+1)	$\frac{x^{2}}{2 \sqrt{x} + 1}$
69710	Evaluate the Integral	integral from -1 to 0 of square root of x-1 with respect to x	$\int_{- 1}^{0} \sqrt{x - 1} d x$
69711	Find the Tangent Line at P=(π/3,1)	y=sec(x)-2cos(x) , P=(pi/3,1)	$y = \sec (x) - 2 \cos (x)$ , $P = (\frac{π}{3}, 1)$
69712	Find the Derivative - d/dx	1-sec(x)	$1 - \sec (x)$
69713	Find the Derivative - d/dx	square root of x square root of x	$\sqrt{x \sqrt{x}}$
69714	Find dy/dv	y=(3-v^2)/(3+v^2)	$y = \frac{3 - v^{2}}{3 + v^{2}}$
69715	Find the Maximum/Minimum Value	y=x^3-12x	$y = x^{3} - 12 x$
69716	Evaluate the Limit	limit as x approaches 3 of (f(x))/(g(x))	$lim_{x \to 3} \frac{f (x)}{g (x)}$
69717	Evaluate the Integral	integral from 1 to square root of 3 of 1/(1+x^2) with respect to x	$\int_{1}^{\sqrt{3}} \frac{1}{1 + x^{2}} d x$
69718	Find the Derivative - d/dx	(9x^2)/(x+2)	$\frac{9 x^{2}}{x + 2}$
69719	Find the Derivative - d/dt	6/5-6/5e^(-20t)	$\frac{6}{5} - \frac{6}{5} e^{- 20 t}$
69720	Find dy/dx	5x^2-xy-4y^2=0	$5 x^{2} - x y - 4 y^{2} = 0$
69721	Find the Derivative - d/dx	(5x^2-3)(x^2+x+4)	$(5 x^{2} - 3) (x^{2} + x + 4)$
69722	Find the Derivative - d/dx	f(x)-g(x)	$f (x) - g (x)$
69723	Evaluate the Integral	integral from 0 to pi/4 of (1+cos(theta)^2)/(cos(theta)^2) with respect to theta	$\int_{0}^{\frac{π}{4}} \frac{1 + \cos^{2} (θ)}{\cos^{2} (θ)} d θ$
69724	Find the Derivative - d/dx	y=(x^2+8x-10)/7	$y = \frac{x^{2} + 8 x - 10}{7}$
69725	Evaluate the Integral	integral from 0 to 3 of (2x-1) with respect to x	$\int_{0}^{3} (2 x - 1) d x$
69726	Evaluate the Integral	integral from -1 to 3 of (3x^2+5x-1) with respect to x	$\int_{- 1}^{3} (3 x^{2} + 5 x - 1) d x$
69727	Evaluate the Limit	limit as h approaches 0 of ( natural log of e+h-1)/h	$lim_{h \to 0} \frac{\ln (e + h) - 1}{h}$
69728	Evaluate the Integral	integral from 0 to 1 of (e^x-e^(-2x)) with respect to x	$\int_{0}^{1} (e^{x} - e^{- 2 x}) d x$
69729	Find the Tangent Line at (1,0)	f(x)=e^(-x) natural log of x , (1,0)	$f (x) = e^{- x} \ln (x)$ , $(1, 0)$
69730	Find dy/dx	y=( square root of x)/(e^x)	$y = \frac{\sqrt{x}}{e^{x}}$
69731	Evaluate the Integral	integral of arcsin(cos(x)) with respect to x	$\int \arcsin (\cos (x)) d x$
69732	Find the Derivative - d/dx	(d^36)/(dx^36)(-7sin(x))	$\frac{d^{36}}{d x^{36}} (- 7 \sin (x))$
69733	Evaluate the Integral	integral from a to b of csc(x) with respect to x	$\int_{a}^{b} \csc (x) d x$
69734	Evaluate the Integral	integral of (4/(x^3)+2/x) with respect to x	$\int (\frac{4}{x^{3}} + \frac{2}{x}) d x$
69735	Evaluate the Integral	integral of ( square root of 1+ square root of x)/( square root of x) with respect to x	$\int \frac{\sqrt{1 + \sqrt{x}}}{\sqrt{x}} d x$
69736	Find the Derivative - d/dx	e^(pix)	$e^{π x}$
69737	Find the Maximum/Minimum Value	f(x)=2sin(3x)	$f (x) = 2 \sin (3 x)$
69738	Find dw/dz	w=7z^2e^z	$w = 7 z^{2} e^{z}$
69739	Evaluate the Integral	integral from -1 to 2 of (f(x)+6x) with respect to x	$\int_{- 1}^{2} (f (x) + 6 x) d x$
69740	Find the Derivative - d/dy	e^(x^2y)	$e^{x^{2} y}$
69741	Find the Maximum/Minimum Value	f(x)=-x^2	$f (x) = - x^{2}$
69742	Integrate Using u-Substitution	integral of e^x square root of 1+e^x with respect to x	$\int e^{x} \sqrt{1 + e^{x}} d x$
69743	Evaluate the Limit	limit as x approaches 3/2 of (8x^3-27)/(2x-3)	$lim_{x \to \frac{3}{2}} \frac{8 x^{3} - 27}{2 x - 3}$
69744	Find the Tangent Line at (0,5)	y=5e^x+x , (0,5)	$y = 5 e^{x} + x$ , $(0, 5)$
69745	Integrate By Parts	integral from 1 to 2 of x natural log of x with respect to x	$\int_{1}^{2} x \ln (x) d x$
69746	Evaluate the Integral	integral of (pi-x)cos(pix) with respect to x	$\int (π - x) \cos (π x) d x$
69747	Find the Derivative - d/dx	y=f(g(x))	$y = f (g (x))$
69748	Evaluate the Limit	limit as w approaches 1 of (1+ cube root of w)(2-w^2+3w^3)	$lim_{w \to 1} (1 + \sqrt[3]{w}) (2 - w^{2} + 3 w^{3})$
69749	Evaluate Using L'Hospital's Rule	limit as x approaches -1 of (2^(x+1)-1)/(sin(pix))	$lim_{x \to - 1} \frac{2^{x + 1} - 1}{\sin (π x)}$
69750	Find dy/dx	xy-x=5	$x y - x = 5$
69751	Find the Tangent Line at (0,6)	y=6e^x+x , (0,6)	$y = 6 e^{x} + x$ , $(0, 6)$
69752	Find the Maximum/Minimum Value	sin(x)+cos(x)	$\sin (x) + \cos (x)$
69753	Evaluate the Summation	sum from n=1 to 3 of a_n+1-a_n	$\sum_{n = 1}^{3} a_{n + 1} - a_{n}$
69754	Find the Derivative - d/dx	limit as h approaches 0 of ( square root of x+h- square root of x)/h	$lim_{h \to 0} \frac{\sqrt{x + h} - \sqrt{x}}{h}$
69755	Find dr/ds	r=1/(3s^2)-6/(5s^4)	$r = \frac{1}{3 s^{2}} - \frac{6}{5 s^{4}}$
69756	Find the Derivative - d/dx	y=(x+1/x)^-1	$y = {(x + \frac{1}{x})}^{- 1}$
69757	Evaluate the Limit	limit as x approaches infinity of (2x^2+3x)/( square root of x^2-x)	$lim_{x \to \infty} \frac{2 x^{2} + 3 x}{\sqrt{x^{2} - x}}$
69758	Find dx/dy	y=(x^3)/(x-1)	$y = \frac{x^{3}}{x - 1}$
69759	Evaluate the Limit	limit as x approaches 0 of (sin(x)+sin(5x))/(6x)	$lim_{x \to 0} \frac{\sin (x) + \sin (5 x)}{6 x}$
69760	Find the Domain and Range	p(x)=-3x+7 if x<=3; x if 3=5	$p (x) = {\begin{cases} - 3 x + 7 & x \leq 3 \\ x & 3 = 5 \end{cases}$
69761	Find the Maximum/Minimum Value	x	$x$
69762	Find dy/dt	y=t( natural log of 1t)^2	$y = t \ln^{2} (1 t)$
69763	Find the Derivative - d/dx	y=(cos(x))/(sin(x)^2)	$y = \frac{\cos (x)}{\sin^{2} (x)}$
69764	Evaluate the Limit	limit as x approaches 2 of 6/(x^2-x-2)-2/(x-2)	$lim_{x \to 2} \frac{6}{x^{2} - x - 2} - \frac{2}{x - 2}$
69765	Find the Tangent Line at (8,0)	y = natural log of x^2-8x+1 , (8,0)	$y = \ln (x^{2} - 8 x + 1)$ , $(8, 0)$
69766	Find the Derivative - d/dx	y=-1/x	$y = - \frac{1}{x}$
69767	Evaluate the Integral	integral of (2x^4+6)^(4/3)x^3 with respect to x	$\int {(2 x^{4} + 6)}^{\frac{4}{3}} x^{3} d x$
69768	Find dy/dx	y = square root of 24+x^2	$y = \sqrt{24 + x^{2}}$
69769	Evaluate the Integral	integral of (3x^2-5x+4) with respect to x	$\int (3 x^{2} - 5 x + 4) d x$
69770	Find the Derivative - d/dx	y=x^2+2/x	$y = x^{2} + \frac{2}{x}$
69771	Find dy/dx	y = square root of x+ square root of x+ square root of x	$y = \sqrt{x + \sqrt{x + \sqrt{x}}}$
69772	Find the Tangent Line at (6,4)	f(x)=((x+2)/(x-2))^2 , (6,4)	$f (x) = {(\frac{x + 2}{x - 2})}^{2}$ , $(6, 4)$
69773	Find the Slope of the Tangent Line at (1,0)	y=x-x^3 , (1,0)	$y = x - x^{3}$ , $(1, 0)$
69774	Integrate Using Trig Substitution	integral of ( square root of 1-x^2)/(x^2) with respect to x	$\int \frac{\sqrt{1 - x^{2}}}{x^{2}} d x$
69775	Find dy/dx	y = square root of 4x+1	$y = \sqrt{4 x + 1}$
69776	Find the Derivative - d/dr	(pir^2h)/3	$\frac{π r^{2} h}{3}$
69777	Evaluate the Limit	limit as x approaches infinity of ( natural log of x)/(x^2)	$lim_{x \to \infty} \frac{\ln (x)}{x^{2}}$
69778	Evaluate the Integral	integral of x( natural log of x)^2 with respect to x	$\int x \ln^{2} (x) d x$
69779	Find the Derivative - d/dx	y = square root of 1+ square root of x	$y = \sqrt{1 + \sqrt{x}}$
69780	Find dy/dx	y=(x^2+4x+3)/( square root of x)	$y = \frac{x^{2} + 4 x + 3}{\sqrt{x}}$
69781	Find the Derivative - d/dx	y=(4x^3-3x^2)/(4x^5-4)	$y = \frac{4 x^{3} - 3 x^{2}}{4 x^{5} - 4}$
69782	Find the Maximum/Minimum Value	f(x)=x^2-25 natural log of x^2	$f (x) = x^{2} - 25 \ln (x^{2})$
69783	Evaluate the Integral	integral of square root of a+bx with respect to x	$\int \sqrt{a + b x} d x$
69784	Evaluate the Integral	integral from 2 to infinity of e^(-5p) with respect to p	$\int_{2}^{\infty} e^{- 5 p} d p$
69785	Use Logarithmic Differentiation to Find the Derivative	y=x^(2/x)	$y = x^{\frac{2}{x}}$
69786	Find dT/dD	T=(C/2-D/3)D^2	$T = (\frac{C}{2} - \frac{D}{3}) D^{2}$
69787	Evaluate the Limit	limit as x approaches infinity of (x^3)/(4x^2+3)	$lim_{x \to \infty} \frac{x^{3}}{4 x^{2} + 3}$
69788	Find dy/dx	x^2-3 natural log of y+y^2=10	$x^{2} - 3 \ln (y) + y^{2} = 10$
69789	Find dy/dx	y = square root of x^3	$y = \sqrt{x^{3}}$
69790	Find dw/dz	w=z^2e^z	$w = z^{2} e^{z}$
69791	Evaluate the Limit	limit as x approaches 0 from the right of (1+x)^(1/x)	$lim_{x \to 0^{+}} {(1 + x)}^{\frac{1}{x}}$
69792	Evaluate the Integral	integral from 0 to t of x square root of x-t with respect to x	$\int_{0}^{t} x \sqrt{x - t} d x$
69793	Evaluate the Limit	limit as x approaches negative infinity of (1+x^6)/(x^4+1)	$lim_{x \to - \infty} \frac{1 + x^{6}}{x^{4} + 1}$
69794	Find the Derivative - d/dx	2cos(x)^2-1	$2 \cos^{2} (x) - 1$
69795	Integrate Using u-Substitution	integral of x/( square root of x+1) with respect to x	$\int \frac{x}{\sqrt{x + 1}} d x$
69796	Evaluate the Limit	limit as x approaches -pi/3 of (-4sin(x))/(-8+5cos(x))	$lim_{x \to - \frac{π}{3}} \frac{- 4 \sin (x)}{- 8 + 5 \cos (x)}$
69797	Find dy/dx	y=(-2x^3-4)^-4	$y = {(- 2 x^{3} - 4)}^{- 4}$
69798	Find the Derivative - d/dx	y=(a^2+x^2)/(a^2-x^2)	$y = \frac{a^{2} + x^{2}}{a^{2} - x^{2}}$
69799	Find dy/dx	cos(xy^2)=y	$\cos (x y^{2}) = y$
69800	Evaluate the Integral	integral from 0 to a of f(x) with respect to x	$\int_{0}^{a} f (x) d x$